Multicollinearity occurs when independent variables are highly
correlated, which can distort the coefficients in a regression model. We
are testing for Multicollinearity with the following techniques:
3.1.2 Multicollinearity: Variance Inflation Factors
So let’s find the VIF for the variables.
#2. Variance Inflation Factors (VIF)
imcdiag(firstordermodel, method="VIF")
##
## Call:
## imcdiag(mod = firstordermodel, method = "VIF")
##
##
## VIF Multicollinearity Diagnostics
##
## VIF detection
## factor(engine_type)Piston 12.5070 1
## factor(engine_type)Propjet 6.5843 0
## engine_power 27.9138 1
## max_speed 4.9745 0
## cruise_speed 10.0485 1
## stall_speed 4.5704 0
## fuel_tank 30.5244 1
## all_eng_roc 2.7720 0
## out_eng_roc 6.7501 0
## takeoff_distance 5.2539 0
## landing_distance 165.2845 1
## empty_weight 138.6177 1
## length 21.4960 1
## wing_span 7.1323 0
## range 5.1477 0
##
## Multicollinearity may be due to factor(engine_type)Piston engine_power cruise_speed fuel_tank landing_distance empty_weight length regressors
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## ===================================
vif(firstordermodel)
## GVIF Df GVIF^(1/(2*Df))
## factor(engine_type) 16.141293 2 2.004401
## engine_power 27.913786 1 5.283350
## max_speed 4.974526 1 2.230365
## cruise_speed 10.048520 1 3.169940
## stall_speed 4.570406 1 2.137851
## fuel_tank 30.524423 1 5.524891
## all_eng_roc 2.772011 1 1.664936
## out_eng_roc 6.750085 1 2.598093
## takeoff_distance 5.253891 1 2.292137
## landing_distance 165.284479 1 12.856301
## empty_weight 138.617698 1 11.773602
## length 21.496040 1 4.636382
## wing_span 7.132325 1 2.670641
## range 5.147730 1 2.268861
From the output we can see that landing_distance has highest VIF.
According to the VIF values, we can list the highest multicollinearity
items as below:
Severe Multicollinearity (VIF/GVIF > 10):
landing_distance (VIF=165.28, GVIF=165.28)
empty_weight (VIF=138.62, GVIF=138.62)
fuel_tank (VIF=30.52, GVIF=30.52)
engine_power (VIF=27.91, GVIF=27.91)
length (VIF=21.50, GVIF=21.50)
factor(engine_type)Piston (VIF=12.51, GVIF=16.14)
cruise_speed (VIF=10.05, GVIF=10.05)
Moderate/Low Collinearity (VIF/GVIF < 10): All other variables
(e.g.,max_speed, wing_span, range) are safe to retain. GVIF (Generalized
Variance Inflation Factor) adjusts for categorical predictors like
engine_type. For categorical variables with Df > 1, e.g., engine_type
has 2 levels, GVIF^(1/(2*Df)) is interpreted. Here, factor(engine_type)
has GVIF^(1/4) = 2.00 → Acceptable (under common thresholds).
So remove the most correlated variables Priority Order:
First: landing_distance (VIF=165.28)
Second: empty_weight (VIF=138.62)
Third: fuel_tank (VIF=30.52)
Fourth: length (VIF=21.50)
Since enigne_power, Cruise_speed and engine_type are statistically
and theoretically significant, we cannot remove them. Below code removes
the variables in the highest collinearity order.
#firstordermodel
model1 = lm(price ~factor(engine_type)+engine_power + max_speed + cruise_speed +stall_speed +
fuel_tank + all_eng_roc + out_eng_roc + takeoff_distance + landing_distance +
empty_weight + length + wing_span + range, data = AircraftData)
summary(model1)
##
## Call:
## lm(formula = price ~ factor(engine_type) + engine_power + max_speed +
## cruise_speed + stall_speed + fuel_tank + all_eng_roc + out_eng_roc +
## takeoff_distance + landing_distance + empty_weight + length +
## wing_span + range, data = AircraftData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -935282 -228459 -47954 191710 1777937
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.653e+04 2.464e+05 -0.067 0.946532
## factor(engine_type)Piston -4.274e+05 1.255e+05 -3.406 0.000714 ***
## factor(engine_type)Propjet -3.642e+05 1.246e+05 -2.923 0.003629 **
## engine_power 8.070e+01 4.566e+01 1.767 0.077814 .
## max_speed 1.794e+03 3.013e+02 5.954 5e-09 ***
## cruise_speed 4.828e+03 4.782e+02 10.096 < 2e-16 ***
## stall_speed 4.041e+03 2.019e+03 2.001 0.045938 *
## fuel_tank 1.166e+01 1.986e+01 0.587 0.557400
## all_eng_roc 8.712e+00 1.766e+01 0.493 0.622036
## out_eng_roc -6.528e+01 3.569e+01 -1.829 0.067983 .
## takeoff_distance 8.075e+01 5.007e+01 1.613 0.107475
## landing_distance -8.968e+01 1.923e+01 -4.664 4e-06 ***
## empty_weight 6.497e+01 3.208e+01 2.025 0.043403 *
## length 1.533e+03 5.108e+02 3.001 0.002827 **
## wing_span 1.412e+03 4.032e+02 3.503 0.000502 ***
## range 1.825e+02 5.045e+01 3.617 0.000329 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 348000 on 491 degrees of freedom
## Multiple R-squared: 0.8868, Adjusted R-squared: 0.8833
## F-statistic: 256.3 on 15 and 491 DF, p-value: < 2.2e-16
imcdiag(model1, method="VIF")
##
## Call:
## imcdiag(mod = model1, method = "VIF")
##
##
## VIF Multicollinearity Diagnostics
##
## VIF detection
## factor(engine_type)Piston 12.5070 1
## factor(engine_type)Propjet 6.5843 0
## engine_power 27.9138 1
## max_speed 4.9745 0
## cruise_speed 10.0485 1
## stall_speed 4.5704 0
## fuel_tank 30.5244 1
## all_eng_roc 2.7720 0
## out_eng_roc 6.7501 0
## takeoff_distance 5.2539 0
## landing_distance 165.2845 1
## empty_weight 138.6177 1
## length 21.4960 1
## wing_span 7.1323 0
## range 5.1477 0
##
## Multicollinearity may be due to factor(engine_type)Piston engine_power cruise_speed fuel_tank landing_distance empty_weight length regressors
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## ===================================
#removed landing_distance
model2 = lm(price ~factor(engine_type)+engine_power + max_speed + cruise_speed +stall_speed +
fuel_tank + all_eng_roc + out_eng_roc + takeoff_distance +
empty_weight + length + wing_span + range, data = AircraftData)
summary(model2)
##
## Call:
## lm(formula = price ~ factor(engine_type) + engine_power + max_speed +
## cruise_speed + stall_speed + fuel_tank + all_eng_roc + out_eng_roc +
## takeoff_distance + empty_weight + length + wing_span + range,
## data = AircraftData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -922389 -230292 -50931 200933 1993660
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 57568.57 251044.88 0.229 0.818719
## factor(engine_type)Piston -448395.55 128035.27 -3.502 0.000504 ***
## factor(engine_type)Propjet -394540.95 127027.84 -3.106 0.002006 **
## engine_power 46.97 46.03 1.020 0.308014
## max_speed 1640.00 305.71 5.365 1.25e-07 ***
## cruise_speed 4772.82 488.07 9.779 < 2e-16 ***
## stall_speed 4845.70 2053.93 2.359 0.018703 *
## fuel_tank -19.76 19.07 -1.036 0.300587
## all_eng_roc 8.86 18.03 0.491 0.623346
## out_eng_roc -54.06 36.35 -1.487 0.137661
## takeoff_distance 57.17 50.86 1.124 0.261460
## empty_weight -60.34 17.90 -3.370 0.000809 ***
## length 1420.64 520.91 2.727 0.006615 **
## wing_span 1302.44 410.90 3.170 0.001621 **
## range 185.46 51.50 3.601 0.000349 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 355300 on 492 degrees of freedom
## Multiple R-squared: 0.8817, Adjusted R-squared: 0.8784
## F-statistic: 262 on 14 and 492 DF, p-value: < 2.2e-16
imcdiag(model2, method="VIF")
##
## Call:
## imcdiag(mod = model2, method = "VIF")
##
##
## VIF Multicollinearity Diagnostics
##
## VIF detection
## factor(engine_type)Piston 12.4909 1
## factor(engine_type)Propjet 6.5664 0
## engine_power 27.2139 1
## max_speed 4.9151 0
## cruise_speed 10.0423 1
## stall_speed 4.5370 0
## fuel_tank 27.0119 1
## all_eng_roc 2.7720 0
## out_eng_roc 6.7194 0
## takeoff_distance 5.2004 0
## empty_weight 41.4192 1
## length 21.4482 1
## wing_span 7.1080 0
## range 5.1469 0
##
## Multicollinearity may be due to factor(engine_type)Piston engine_power cruise_speed fuel_tank empty_weight length regressors
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## ===================================
#removed empty_weight
model3 = lm(price ~factor(engine_type)+engine_power + max_speed + cruise_speed +stall_speed +
fuel_tank + all_eng_roc + out_eng_roc + takeoff_distance + length + wing_span + range,
data = AircraftData)
summary(model3)
##
## Call:
## lm(formula = price ~ factor(engine_type) + engine_power + max_speed +
## cruise_speed + stall_speed + fuel_tank + all_eng_roc + out_eng_roc +
## takeoff_distance + length + wing_span + range, data = AircraftData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1010722 -228791 -53279 207544 1884293
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 569816.12 201901.75 2.822 0.00496 **
## factor(engine_type)Piston -613204.07 119567.06 -5.129 4.20e-07 ***
## factor(engine_type)Propjet -588560.93 114419.57 -5.144 3.89e-07 ***
## engine_power -27.66 40.78 -0.678 0.49794
## max_speed 1494.70 305.82 4.888 1.38e-06 ***
## cruise_speed 4620.14 491.04 9.409 < 2e-16 ***
## stall_speed 2996.44 1999.99 1.498 0.13471
## fuel_tank -50.73 16.89 -3.004 0.00280 **
## all_eng_roc 14.36 18.14 0.791 0.42916
## out_eng_roc -37.31 36.39 -1.025 0.30571
## takeoff_distance 41.29 51.17 0.807 0.42006
## length 921.06 504.59 1.825 0.06855 .
## wing_span 894.18 396.75 2.254 0.02465 *
## range 207.97 51.60 4.031 6.44e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 359000 on 493 degrees of freedom
## Multiple R-squared: 0.879, Adjusted R-squared: 0.8758
## F-statistic: 275.5 on 13 and 493 DF, p-value: < 2.2e-16
imcdiag(model3, method="VIF")
##
## Call:
## imcdiag(mod = model3, method = "VIF")
##
##
## VIF Multicollinearity Diagnostics
##
## VIF detection
## factor(engine_type)Piston 10.6691 1
## factor(engine_type)Propjet 5.2179 0
## engine_power 20.9170 1
## max_speed 4.8173 0
## cruise_speed 9.9558 0
## stall_speed 4.2133 0
## fuel_tank 20.7414 1
## all_eng_roc 2.7493 0
## out_eng_roc 6.5939 0
## takeoff_distance 5.1557 0
## length 19.7116 1
## wing_span 6.4903 0
## range 5.0603 0
##
## Multicollinearity may be due to factor(engine_type)Piston engine_power fuel_tank length regressors
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## ===================================
#removed fuel_tank
model4 = lm(price ~factor(engine_type)+engine_power + max_speed + cruise_speed +stall_speed +
all_eng_roc + out_eng_roc + takeoff_distance + length + wing_span + range,
data = AircraftData)
summary(model4)
##
## Call:
## lm(formula = price ~ factor(engine_type) + engine_power + max_speed +
## cruise_speed + stall_speed + all_eng_roc + out_eng_roc +
## takeoff_distance + length + wing_span + range, data = AircraftData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1310103 -225685 -48704 196659 1939134
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 695908.97 199089.37 3.495 0.000516 ***
## factor(engine_type)Piston -641222.25 120167.30 -5.336 1.45e-07 ***
## factor(engine_type)Propjet -560763.09 114967.61 -4.878 1.45e-06 ***
## engine_power -126.51 24.28 -5.211 2.76e-07 ***
## max_speed 1467.85 308.16 4.763 2.51e-06 ***
## cruise_speed 4637.80 494.98 9.370 < 2e-16 ***
## stall_speed 3901.87 1993.15 1.958 0.050834 .
## all_eng_roc 18.96 18.22 1.040 0.298814
## out_eng_roc -60.79 35.83 -1.697 0.090357 .
## takeoff_distance 73.95 50.40 1.467 0.142949
## length 954.72 508.55 1.877 0.061062 .
## wing_span 622.99 389.47 1.600 0.110330
## range 154.44 48.82 3.164 0.001654 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 361900 on 494 degrees of freedom
## Multiple R-squared: 0.8768, Adjusted R-squared: 0.8738
## F-statistic: 293 on 12 and 494 DF, p-value: < 2.2e-16
imcdiag(model4, method="VIF")
##
## Call:
## imcdiag(mod = model4, method = "VIF")
##
##
## VIF Multicollinearity Diagnostics
##
## VIF detection
## factor(engine_type)Piston 10.6042 1
## factor(engine_type)Propjet 5.1838 0
## engine_power 7.2957 0
## max_speed 4.8132 0
## cruise_speed 9.9544 0
## stall_speed 4.1176 0
## all_eng_roc 2.7298 0
## out_eng_roc 6.2897 0
## takeoff_distance 4.9230 0
## length 19.7019 1
## wing_span 6.1544 0
## range 4.4570 0
##
## Multicollinearity may be due to factor(engine_type)Piston length regressors
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## ===================================
#removed length
model5 = lm(price ~factor(engine_type)+engine_power + max_speed + cruise_speed +stall_speed +
all_eng_roc + out_eng_roc + takeoff_distance + wing_span + range, data = AircraftData)
summary(model5)
##
## Call:
## lm(formula = price ~ factor(engine_type) + engine_power + max_speed +
## cruise_speed + stall_speed + all_eng_roc + out_eng_roc +
## takeoff_distance + wing_span + range, data = AircraftData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1291854 -224274 -51822 188629 2036117
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 723802.03 199039.77 3.636 0.000305 ***
## factor(engine_type)Piston -670177.36 119476.86 -5.609 3.38e-08 ***
## factor(engine_type)Propjet -547492.38 115042.31 -4.759 2.56e-06 ***
## engine_power -107.82 22.20 -4.858 1.60e-06 ***
## max_speed 1522.64 307.56 4.951 1.02e-06 ***
## cruise_speed 4702.09 495.05 9.498 < 2e-16 ***
## stall_speed 4695.48 1952.76 2.405 0.016559 *
## all_eng_roc 21.87 18.20 1.202 0.230105
## out_eng_roc -44.91 34.90 -1.287 0.198788
## takeoff_distance 75.07 50.53 1.486 0.137965
## wing_span 1094.87 298.26 3.671 0.000268 ***
## range 166.44 48.52 3.430 0.000653 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 362800 on 495 degrees of freedom
## Multiple R-squared: 0.8759, Adjusted R-squared: 0.8732
## F-statistic: 317.7 on 11 and 495 DF, p-value: < 2.2e-16
imcdiag(model5, method="VIF")
##
## Call:
## imcdiag(mod = model5, method = "VIF")
##
##
## VIF Multicollinearity Diagnostics
##
## VIF detection
## factor(engine_type)Piston 10.4295 1
## factor(engine_type)Propjet 5.1642 0
## engine_power 6.0686 0
## max_speed 4.7700 0
## cruise_speed 9.9067 0
## stall_speed 3.9324 0
## all_eng_roc 2.7099 0
## out_eng_roc 5.9389 0
## takeoff_distance 4.9223 0
## wing_span 3.5910 0
## range 4.3806 0
##
## Multicollinearity may be due to factor(engine_type)Piston regressors
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## ===================================
# removed insignifocant terms:all_eng_roc, out_eng_roc & takeoff_distance from model5
model6 = lm(price ~factor(engine_type)+engine_power + max_speed + cruise_speed +stall_speed +
wing_span + range, data = AircraftData)
summary(model6)
##
## Call:
## lm(formula = price ~ factor(engine_type) + engine_power + max_speed +
## cruise_speed + stall_speed + wing_span + range, data = AircraftData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1305416 -227626 -54056 193438 2121608
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 693659.32 186978.43 3.710 0.000231 ***
## factor(engine_type)Piston -661350.47 111533.27 -5.930 5.68e-09 ***
## factor(engine_type)Propjet -527735.55 110064.68 -4.795 2.15e-06 ***
## engine_power -115.72 21.27 -5.441 8.31e-08 ***
## max_speed 1571.61 305.17 5.150 3.76e-07 ***
## cruise_speed 4963.33 474.50 10.460 < 2e-16 ***
## stall_speed 5401.47 1817.88 2.971 0.003109 **
## wing_span 1104.12 288.70 3.825 0.000148 ***
## range 159.60 47.52 3.359 0.000843 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 363200 on 498 degrees of freedom
## Multiple R-squared: 0.8749, Adjusted R-squared: 0.8729
## F-statistic: 435.3 on 8 and 498 DF, p-value: < 2.2e-16
imcdiag(model6, method="VIF")
##
## Call:
## imcdiag(mod = model6, method = "VIF")
##
##
## VIF Multicollinearity Diagnostics
##
## VIF detection
## factor(engine_type)Piston 9.0677 0
## factor(engine_type)Propjet 4.7161 0
## engine_power 5.5579 0
## max_speed 4.6856 0
## cruise_speed 9.0803 0
## stall_speed 3.4000 0
## wing_span 3.3566 0
## range 4.1923 0
##
## NOTE: VIF Method Failed to detect multicollinearity
##
##
## 0 --> COLLINEARITY is not detected by the test
##
## ===================================
# removed cruise_speed: even if the multicollinearity =0 , VIF>5, so removed from model5
model7 = lm(price ~factor(engine_type)+engine_power + max_speed + stall_speed + all_eng_roc + out_eng_roc +
takeoff_distance + wing_span + range, data = AircraftData)
summary(model7)
##
## Call:
## lm(formula = price ~ factor(engine_type) + engine_power + max_speed +
## stall_speed + all_eng_roc + out_eng_roc + takeoff_distance +
## wing_span + range, data = AircraftData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1352143 -252725 -53828 229130 1554800
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.390e+06 2.023e+05 6.868 1.96e-11 ***
## factor(engine_type)Piston -1.207e+06 1.144e+05 -10.551 < 2e-16 ***
## factor(engine_type)Propjet -1.019e+06 1.127e+05 -9.035 < 2e-16 ***
## engine_power -1.130e+02 2.410e+01 -4.686 3.60e-06 ***
## max_speed 2.389e+03 3.191e+02 7.487 3.24e-13 ***
## stall_speed 1.040e+04 2.018e+03 5.151 3.74e-07 ***
## all_eng_roc 6.346e+01 1.919e+01 3.306 0.00101 **
## out_eng_roc -6.729e+01 3.782e+01 -1.779 0.07587 .
## takeoff_distance 1.503e+02 5.420e+01 2.774 0.00575 **
## wing_span 9.717e+02 3.237e+02 3.002 0.00282 **
## range 2.791e+02 5.111e+01 5.460 7.53e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 394100 on 496 degrees of freedom
## Multiple R-squared: 0.8533, Adjusted R-squared: 0.8503
## F-statistic: 288.5 on 10 and 496 DF, p-value: < 2.2e-16
#imcdiag(model7, method="VIF")
# removed insignifocant terms:out_eng_roc from model6
model8 = lm(price ~factor(engine_type)+engine_power + max_speed + stall_speed +
all_eng_roc + takeoff_distance + wing_span + range, data = AircraftData)
summary(model8)
##
## Call:
## lm(formula = price ~ factor(engine_type) + engine_power + max_speed +
## stall_speed + all_eng_roc + takeoff_distance + wing_span +
## range, data = AircraftData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1380009 -248912 -51757 236662 1520550
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.282e+06 1.934e+05 6.625 9.02e-11 ***
## factor(engine_type)Piston -1.144e+06 1.091e+05 -10.489 < 2e-16 ***
## factor(engine_type)Propjet -9.659e+05 1.090e+05 -8.860 < 2e-16 ***
## engine_power -1.240e+02 2.333e+01 -5.316 1.61e-07 ***
## max_speed 2.383e+03 3.197e+02 7.453 4.08e-13 ***
## stall_speed 1.020e+04 2.020e+03 5.051 6.19e-07 ***
## all_eng_roc 6.615e+01 1.918e+01 3.449 0.00061 ***
## takeoff_distance 1.001e+02 4.636e+01 2.159 0.03134 *
## wing_span 1.036e+03 3.224e+02 3.213 0.00140 **
## range 2.709e+02 5.101e+01 5.310 1.65e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 395000 on 497 degrees of freedom
## Multiple R-squared: 0.8524, Adjusted R-squared: 0.8497
## F-statistic: 318.8 on 9 and 497 DF, p-value: < 2.2e-16
imcdiag(model7, method="VIF")
##
## Call:
## imcdiag(mod = model7, method = "VIF")
##
##
## VIF Multicollinearity Diagnostics
##
## VIF detection
## factor(engine_type)Piston 8.0988 0
## factor(engine_type)Propjet 4.2041 0
## engine_power 6.0650 0
## max_speed 4.3507 0
## stall_speed 3.5607 0
## all_eng_roc 2.5532 0
## out_eng_roc 5.9119 0
## takeoff_distance 4.8012 0
## wing_span 3.5842 0
## range 4.1191 0
##
## NOTE: VIF Method Failed to detect multicollinearity
##
##
## 0 --> COLLINEARITY is not detected by the test
##
## ===================================
Proceeding with model 5, since the multicollinearity removed.
model5 = lm(price ~factor(engine_type)+engine_power + max_speed + cruise_speed +stall_speed +
all_eng_roc + out_eng_roc + takeoff_distance + wing_span + range, data = AircraftData)
summary(model5)
##
## Call:
## lm(formula = price ~ factor(engine_type) + engine_power + max_speed +
## cruise_speed + stall_speed + all_eng_roc + out_eng_roc +
## takeoff_distance + wing_span + range, data = AircraftData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1291854 -224274 -51822 188629 2036117
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 723802.03 199039.77 3.636 0.000305 ***
## factor(engine_type)Piston -670177.36 119476.86 -5.609 3.38e-08 ***
## factor(engine_type)Propjet -547492.38 115042.31 -4.759 2.56e-06 ***
## engine_power -107.82 22.20 -4.858 1.60e-06 ***
## max_speed 1522.64 307.56 4.951 1.02e-06 ***
## cruise_speed 4702.09 495.05 9.498 < 2e-16 ***
## stall_speed 4695.48 1952.76 2.405 0.016559 *
## all_eng_roc 21.87 18.20 1.202 0.230105
## out_eng_roc -44.91 34.90 -1.287 0.198788
## takeoff_distance 75.07 50.53 1.486 0.137965
## wing_span 1094.87 298.26 3.671 0.000268 ***
## range 166.44 48.52 3.430 0.000653 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 362800 on 495 degrees of freedom
## Multiple R-squared: 0.8759, Adjusted R-squared: 0.8732
## F-statistic: 317.7 on 11 and 495 DF, p-value: < 2.2e-16
imcdiag(model5, method="VIF")
##
## Call:
## imcdiag(mod = model5, method = "VIF")
##
##
## VIF Multicollinearity Diagnostics
##
## VIF detection
## factor(engine_type)Piston 10.4295 1
## factor(engine_type)Propjet 5.1642 0
## engine_power 6.0686 0
## max_speed 4.7700 0
## cruise_speed 9.9067 0
## stall_speed 3.9324 0
## all_eng_roc 2.7099 0
## out_eng_roc 5.9389 0
## takeoff_distance 4.9223 0
## wing_span 3.5910 0
## range 4.3806 0
##
## Multicollinearity may be due to factor(engine_type)Piston regressors
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
##
## ===================================
plot(~price +factor(engine_type)+engine_power + max_speed + cruise_speed +stall_speed +
all_eng_roc + out_eng_roc + takeoff_distance + wing_span + range, data = AircraftData)
